Monochromatic light is normally incident on a diffraction grating. The mth order line is at a angle of diffraction θ and has width w. A wide single slit is now placed in front of the grating and its width is then slowly reduced. As a
the ans. is: θ remains the same and w increases
Can someone help me solve this?
To understand why the angle of diffraction remains the same and the width increases when a wide single slit is placed in front of the grating, we need to consider how a diffraction grating works and how a single slit affects the diffraction pattern.
A diffraction grating consists of a large number of equally spaced parallel slits or grooves. When monochromatic light is incident on a diffraction grating, it diffracts (spreads out) into multiple orders of spectral lines. Each order corresponds to a different angle of diffraction, which is determined by the spacing of the slits and the wavelength of the light.
Now, when a wide single slit is placed in front of the grating, it acts as a secondary source of diffraction. The single slit itself diffracts the incident light, creating a diffraction pattern with a central maximum (bright spot) surrounded by alternating dark and bright fringes.
As the width of the single slit is reduced, the overall diffraction pattern becomes narrower. However, the position of the mth order line on the grating remains the same. This is because the angle of diffraction only depends on the spacing of the grating and the wavelength of the incident light, which are not affected by the single slit.
The width of the mth order line, on the other hand, increases as the width of the single slit decreases. This is because the broader the single slit, the more light can pass through, resulting in a wider diffraction pattern on the grating.
So, in summary, when a wide single slit is placed in front of a diffraction grating, the angle of diffraction remains the same (θ), while the width of the mth order line (w) increases as the width of the single slit is reduced.